Adler cites as a comparandum Lexicon Ambrosianum 22, 23, 28.
[1] This suppletion is suggested by the corresponding entry in the Lexicon of pseudo-Zonaras 5.1, which is identical to this entry apart from the headword phrase: vs. *)aba/nteios here, ps.-Zonaras has *)aba/nteios do/mos ('Abantian house'). The headword here could serve as a modifier for any substantive of the masculine gender, including a son or descendant, as is suggested by the subsequent reference to a patronymic form. The adjective is unattested outside of grammars and lexica, and ps.-Zonaras provides the only example of it modifying a specific substantive. Stephanus of Byzantium in his entry on 'Abantis', an early name for Euboea (cf. Hesiod fr. 296 Merkelbach-West), notes it as the possessive adjective relating to the Abantes or to their legendary founder Abas, whom Stephanos identifies either as the son of Lynkeus (see note 2 below) or a homonymous son of Poseidon. Cf. also Herodianus Peri orthographias 3.2.429.34 and 465.14.
[2] Not the Abas of alpha 20, but one of the mythological figures of that name; in fact almost certainly A. the son of Lynkeus, king of Argos [Myth, Place] after Danaos and father of the twins Akrisios and Proitos (Pausanias 2.16.2 (web address 1); Apollodorus, Library 2.2.1 (web address 2)).
[3] This term is used by (e.g.) Ovid both for an actual son of Abas (Metamorphoses 4.607 (Acrisius): web address 3) and in the sense of a more distant descendant (4.673 (Perseus, great-grandson of Abas; cf. pi 1372): web address 4).

Same entry, according to Adler, in the Ambrosian Lexicon (74), and cf. more generally the scholia to Apollonius Rhodius, Argonautica 1.932 (where the genitive case occurs), on which see further below.
Abarnis lay on the southern shore of the Propontis (Sea of Marmara), between Parion and Lampsakos; Barrington Atlas map 51 grid H4. According to Stephanus of Byzantium s.v. *)/abarnos (sic), Abarnos and Aparnis were also attested versions of its name.
A scholium to Apollonius Rhodius, Argonautica 1.932 (repeated in more legible form in Etymologicum Magnum 2.11-28) provides an etymological explanation of the origin of the name in Aphrodite's refusal (a)parnh/sasqai) to recognize her offspring Priapos, who was born in the region.

For the etymology of the (rare) headword adjective cf. beta 167, beta 168, beta 169.
[1] Josephus, Jewish War 1.192 (see web address 1 below). For Antipater, father of Herod the Great, see OCD(4) s.v. Antipater(6), pp.107-8. 'Caesar' is Julius Caesar. Mithradates is not one of the six kings of Pontus who bore that name (cf. mu 1044) but the half-caste son of the last of them: a.k.a. M. of Pergamum.

The headword is the neuter singular form of this adjective, which, as a substantive, can be used for the adyton of a temple or shrine.
[1] Up to this point the entry = Synagoge alpha5, and Photius, Lexicon alpha31 Theodoridis; cf. Hesychius alpha91 (where Latte confidently asserts that the headword is quoted from Euripides, Bacchae 10).